Benders Decomposition for Profit Maximizing Hub Location Problems with Capacity Allocation

Abstract

This paper models capacity allocation decisions within profit maximizing hub location problems to satisfy demand of commodities from different market segments. A strong deterministic formulation of the problem is presented and two exact algorithms based on a Benders reformulation are described to solve large-size instances of the problem. A new methodology is developed to strengthen the Benders optimality cuts by decomposing the subproblem in a two-phase fashion. The algorithms are enhanced by the integration of improved variable fixing techniques. The deterministic model is further extended by considering uncertainty associated with the demand to develop a two-stage stochastic program. To solve the stochastic version, a Monte-Carlo simulation-based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithms. Novel acceleration techniques are presented to improve the convergence of the algorithms proposed for the stochastic version. The efficiency and robustness of the algorithms are evaluated through extensive computational experiments. Computational results show that large-scale instances with up to 500 nodes and three demand segments can be solved to optimality, and that the proposed algorithms generate cuts that provide significant speedups compared to using Pareto-optimal cuts. The proposed two-phase methodology for solving the Benders subproblem as well as the variable fixing and acceleration techniques can be used to solve other discrete location and network design problems.